Radar-based hand gesture recognition is an emerging field valued for its contactless and robust capabilities in human-computer interaction (HCI), signal processing, and computer vision [1] [2]. Despite its growing importance, the accuracy of hand gesture recognition remains insufficient [12]. HCI using dynamic hand gesture recognition is potentially an effective and natural method for a user to control a device. The hypothesis of the research in this area is that radar-based gesture recognition will be more effective than vision-based methods, because they are not susceptible to light conditions, and can detect and classify targets, providing rich Doppler information [7]. Its applications include enhancing accessibility in assistive technologies, improving smart device control, and enabling touch-less interfaces for healthcare and industrial environments. Various deep neural network architectures, such as multi-layer perceptrons (MLP) [4], convolutional neural networks (CNN) [5], recurrent neural networks (RNN) [6] and combinations like CNN-RNN [17], have been explored. However, these methods often handle radar images, which are naturally complex-valued (CV), using real-valued (RV) techniques. So far, researchers approaches often involve splitting CV numbers into real and imaginary parts, this can lead to increased network parameters and loss of correlation between these components. CV networks, though potentially richer in representation, face challenges due to a lack of necessary building blocks and therefore has not been utilised much. To address these issues and develop CV building blocks, we developed a novel CV algorithm for two-layer CV-CNN, performing all operations in the complex domain. Our model was tested on two hand gesture radar datasets, achieving 99% accuracy in binary classification for both datasets. The training converged much faster than the corresponding RV-CNN model and number of training parameters is half of RV-CNN.